Differentiation

Practice Questions (Step-by-Step Solutions) Question 1 Find the derivative of [y] w.r.t [x] [x = t^2], [y = \sin t]

1. Statement of the Concept If both [x] and [y] are expressed as functions of another variable (parameter) [t], i.e.,

Practice Questions with Step-by-Step Solutions Question 1 Find [\dfrac{dy}{du}] if [y=x^{3}+2x] and [u=x^{2}+1]. Step-by-step Solution: Compute [\dfrac{dy}{dx}]: [\dfrac{d}{dx}\big(x^{3}+2x\big)][=3x^{2}+2]. Compute [\dfrac{du}{dx}]:

1. Concept Overview Sometimes we need to differentiate one function with respect to another function, instead of differentiating both with

1. What is an Infinite Series? An infinite series is the sum of infinitely many terms: [y = a_{1} +

Practice Questions (with Step-by-Step Solutions) Question 1. Differentiate [y = x^{x}], [x>0]. Step-by-Step Solution: Take natural log of both sides:

1. Why Logarithmic Differentiation? Some functions are difficult to differentiate directly, such as: Functions with variables in both base and

1. What is an Implicit Function? A function where y is not explicitly isolated in the form [y = f(x)],